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Fig. 8.11. Mixing in an unbaffled rotating drum. (a) Dependence of the number of rotations required to reach an entropy of mixing of 0.9 on the ratio of the bed top area to bed volume. The data are from a table presented by Schutyser et al. (2001), adapted with kind permission from John Wiley & Sons, Inc. (b) Equation (8.2) is expressed in terms of Qat, the angle subtended at the center of the drum by the bed surface, as shown on the left. Note that V and A represent volume and area, respectively. The graph on the right shows Qa as a function of the fraction of the drum occupied by the bed, according to Eq. (8.4)

Note that the ratio of exposed surface area to bed volume can be calculated as (Schutyser et al. 2001):

where D is the drum diameter (m) and Bm is the angle in radians subtended at the center by the bed surface for a particular fractional filling a (m3-bed m-3-total-bioreactor-volume). Note that da can be determined from the following relationship:

Unfortunately it is not possible to isolate da on the left hand side of this equation. However, it is possible to use this equation to plot da against co and to fit a polynomial equation. Doing this for values of co from 0 to 0.5 gives the following explicit equation for da in terms of co (Fig. 8.11(b)):

0m = -3412®6 + 6461.3a5 - 4738.7®4 + 1697.5®5 - 310.36®2 + 31.5670+ 0.326. (8.4)

For unbaffled drums, for a particular fractional filling (©), Eqs. (8.2) and (8.4) can be used to calculate RB, which in turn can be compared against Fig. 8.11(a) in order to evaluate the effectiveness of radial mixing that can be expected.

Schutyser et al. (2001) did simulations to investigate the degree to which baffles affect mixing. They compared baffles of 5 cm and 10 cm width within a 30 cm diameter drum, fitting four straight baffles around the inner circumference of the drum (in the manner shown in Fig. 8.1). The smaller baffles had little effect in increasing mixing in the tumbling regime, although at low rotation rates they helped to prevent slumping flow. The larger baffles did improve the effectiveness of mixing.

Schutyser et al. (2002) extended the discrete-particle modeling approach to three dimensions and used it to analyze radial and axial mixing in three different drum designs: a drum without baffles, a drum with four straight baffles (each with a width of 66% of the drum radius) and curved baffles. Straight large baffles do increase axial mixing compared to that in an unbaffled drum, even though they are not designed specifically to push substrate along the axis of the drum. Schutyser et al. (2002) attributed this effect to the higher particle velocities that occur at the surface of the bed. The best design for good axial and radial mixing is a drum with curved baffles, in which the substrate is well mixed axially after three to four rotations. In the same drum without baffles, it can require of the order of 50 to 100 rotations for the bed to be well mixed in the axial direction. Schutyser et al. (2002) noted that with curved baffles it is interesting to incline the central axis of the drum (Fig. 8.12). It can be inclined up until the dynamic angle of repose of the solid, which in their case was 35°, although they suggested that 20° might be more appropriate.

Fig. 8.12. (a) The use of angled baffles and an inclined axis in order to promote axial mixing within a rotating drum bioreactor (Schutyser et al. 2002). Only two baffles are shown, but more can be fitted. (b) The dynamic angle of repose of an agitated bed of solids, which represents an upper limit on the inclination of the drum axis that should be used. Adapted from Schutyser et al. (2002) with kind permission from John Wiley & Sons, Inc.

Fig. 8.12. (a) The use of angled baffles and an inclined axis in order to promote axial mixing within a rotating drum bioreactor (Schutyser et al. 2002). Only two baffles are shown, but more can be fitted. (b) The dynamic angle of repose of an agitated bed of solids, which represents an upper limit on the inclination of the drum axis that should be used. Adapted from Schutyser et al. (2002) with kind permission from John Wiley & Sons, Inc.

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